17/3 : 7 = x : 7/38

To solve the proportion \( \frac{17/3}{7} = \frac{x}{7/38} \), we can use cross-multiplication.

Cross-multiplying gives us:

\[ (17/3) \times (7/38) = x \times 7 \]

Now, calculate the left side:

\[ \frac{17 \cdot 7}{3 \cdot 38} = \frac{119}{114} \]

Now we have:

\[ \frac{119}{114} = 7x \]

To isolate \( x \), we can divide both sides by 7:

\[ x = \frac{119}{114 \cdot 7} = \frac{119}{798} \]

Therefore, the value of \( x \) is:

\[ x = \frac{119}{798} \]

If you want to simplify \( \frac{119}{798} \), you can divide both the numerator and the denominator by their greatest common divisor, which is 7:

\[ x = \frac{119 \div 7}{798 \div 7} = \frac{17}{114} \]

Thus, the final answer is:

\[ x = \frac{17}{114} \]